Answer
Center = $(2,0)$
Radius = $2$
Work Step by Step
For $\theta=\pi/2,\ r=0$, so the origin is on the circle.
A circle passing through the origin, of radius $a$, centered at $P_{0}(r_{0}, \theta_{0}),$
has the polar equation$ \quad r=2a\cos(\theta-\theta_{0})$
$2a=4$, so the radius is $r_{0}=2$.
Also, $(\theta-\theta_{0})=\theta=(\theta-0)$,
so $\theta_{0}=0$ (the center lies on the +x axis)
Center = $(2,0)$
Radius = $2$
